Chaotic gravitational constants for the gravitational search algorithm

• Published in: Applied soft computing Vol. 53; pp. 407 - 419
• Main Authors: Mirjalili, Seyedali, Gandomi, Amir H.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2017
• Subjects: Chaos theory; Chaotic map; Gravitational search algorithm; Population-based algorithm; Sinusoidal map; Gravitational search algorithm; Chaotic map; Chaos theory; Sinusoidal map; Population-based algorithm
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2017.01.008

[Display omitted] •Chaotic maps have been embedded into Gravitational Search Algorithms (GSA) for the first time.•The problem of trapping in local minima in GSA has been improved by the chaotic maps.•The convergence rate of GSA has been improved.•The statistical test allowed us to judge about the significance of the results.•An adaptive normalization is proposed to smoothly transit from the exploration phase to the exploitation phase. In a population-based meta-heuristic, the search process is divided into two main phases: exploration versus exploitation. In the exploration phase, a random behavior is fruitful to explore the search space as extensive as possible. In contrast, a fast exploitation toward the promising regions is the main objective of the latter phase. It is really challenging to find a proper balance between these two phases because of the stochastic nature of population-based meta-heuristic algorithms. The literature shows that chaotic maps are able to improve both phases. This work embeds ten chaotic maps into the gravitational constant (G) of the recently proposed population-based meta-heuristic algorithm called Gravitational Search Algorithm (GSA). Also, an adaptive normalization method is proposed to transit from the exploration phase to the exploitation phase smoothly. As case studies, twelve shifted and biased benchmark functions evaluate the performance of the proposed chaos-based GSA algorithms in terms of exploration and exploitation. A statistical test called Wilcoxon rank-sum is done to judge about the significance of the results as well. The results demonstrate that sinusoidal map is the best map for improving the performance of GSA significantly.